The three dimensional imaging of a small cell by an extended form of X-ray crystallography (or equivalently the development and use of a soft X-ray diffraction microscope for use in cell biology) is proposed. This instrument is designed to provide three-dimensional images of frozen hydrated cellular and sub-cellular structures at better than 20 nm resolution. The instrument does not use optical elements to form the image instead it records the diffraction pattern of the coherently illuminated object, and using techniques borrowed from crystallography, performs the reconstruction using an iterative algorithm. This way the resolution is not limited by the optics, and future developments should improve the resolution limit further. The diffraction pattern from a non-crystalline specimen is a continuous (speckle) pattern. Unlike the case with crystals this pattern contains sufficient information to overcome the phase problem of crystallography by sampling the diffraction pattern at a finer scale. Undulator radiation at the National Synchrotron Light Source is used to provide coherent illumination of the specimen. The diffraction pattern is recorded using a CCD detector. Special care is taken to shield the detector from all but the desired information. A single pattern yields a two-dimensional image. To obtain three-dimensional reconstruction the specimen is rotated and a set of diffraction patterns is collected. Frozen hydrated specimens are used to minimize the effects of radiation damage.